The Grand Isle borrow pit geometry and shoreline were used to evaluate the

methodology described in this thesis (RCPWAVE and DNRBS). The sediment size is

0.2mm and the base conditions for the following cases are a water depth, h, of 15 feet,

incident waves with a wave height of 1.5 feet and a period of 5.6 seconds. The profile

landward of borrow pit was represented as an equilibrium beach profile. The initial

computational domain is shown in Figure 6.5. The length in the longshore direction

encompasses 343 cells, 35 m each of length, for a total of 12,005 m, and the modeled

length in the cross-shore direction comprises 80 cells, 28.75 m width each, for a total of

2300 m. The time step is 1000 seconds. Two cases with different wave angles were

examined.

1. Wave angle =0.0 degree

2. Wave angle=6.5 degree

z
X

Figure 6.5 Computational domain for bathymetry and wave direction
The length in the longshore direction encompasses 343 cells, 35 m each of length, for
a total of 12,005 m, and the modeled length in the cross-shore direction comprises 80
cells, 28.75 m width each, for a total of 2300 m at Grand Isle

12000

11000

10000

9000

, 8000

7000

6000

5000

4000

3000

2000

1000

0

I I

I I I

I I I I I

-10 0 10
Shoreline Change (m)

Figure 6.6 Shoreline changes for a normal incident wave before smoothing
(Pit centerline at 6000 m offshore)
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds at Grand Isle)

Figure 6.6 shows the calculated shoreline evolution with time for a normally incident

wave. It is seen that the shoreline changes are quite irregular and this irregular pattern

remains even for large time. Comparison with the real shoreline demonstrates that this

result is not physically correct. To examine the cause of this effect, the breaking wave

conditions were examined. Figure 6.7 shows the wave angle change at the breaker line

where is seen that the wave angle varies smoothly, thus this is not the source of the

~c-

31

irregularity. The wave angle here has been averaged using three points to reduce any

oscillations, i.e.

(6.1)

12000

11000

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

-10

Pit Centerline

`-------~_ ----_

I I I I i i

I I I I I I I I I I

-5 0 5 11
Breaking Wave Angle (degree)

Figure 6.7 Wave angle at the breaker line before smoothing
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds at Grand Isle)

Figure 6.8 shows the wave height at the breaking line where it is evident that the

wave height varies significantly over small longshore distances. This type of oscillation is

believed to be physically unrealistic, because the large gradients will be smoothed by

ai = 1/ 3(a,_ + a, + a,,)

32

diffraction and possibly other processes. In the RCPWAVE model, there is no smoothing

although diffraction is represented. This character suggests that to obtain correct results,

these large gradients should be smoothed.

12000

11000

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

.

Pit Centerline

, I , I

0.4 0.6 0.8
Breaking Wave Height (m)

Figure 6.8 Breaking wave height before smoothing at Grand Isle
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds at Grand Isle)

. 1 1 1 ,,1 ,,,

IIIIHII

ri l l ll.l.l l T

2

I

Figure 6.2 shows the pit geometry used to conduct the computations. There are sharp

changes in the beach bathymetry and these sharp changes may cause large gradients in

the solution. To verify this possibility, the beach bathymetry is smoothed using the

following equation

h,j = 1/ 8(h,_-1 + 4h,, + hi+, + h,_j- + h,,J) (6.2)

To obtain smoother results, the original bathymetry is averaged 100 times using

Equation (6.2). This equation will not change the total amount of sand excavated from the

pit; however, the maximum depth is decreased.

Figure 6.9 shows the computational domain after the smoothing and Figure 6.10 shows

the wave height at the breaker line where it is seen that the wave height is much smoother

than in Figure 6.8. Figure 6.11 shows the wave angle at the breaker line which is very

similar to that in Figure 6.7. It is quite interesting that smoothing the bathymetry seems to

have a considerable smoothing effect on the breaking wave height but a relatively small

effect on the wave angle. Figure 6.12 shows the calculated shoreline change. Because the

RCPWAVE model only includes the effects of wave refraction and diffraction, and not

wave reflection and dissipation, this result is opposite to that appearing in Figure 6.3 for

6.5 degrees which is also opposite to the actual case which has two erosional cold spots

and three erosional hot spots.

Figure 6.14 depicts wave directions and wave rays in the vicinity of the smoothed pit.

It can be noted that in the center of pit the direction of wave rays is towards inside which

associated with an erosional cold spot and the direction of wave ray near the ends of pit is

toward outside which related to forming erosional hot spots.

Z

x

Figure 6.9 Bathymetry after smoothing at Grand Isle
The length in the longshore direction encompasses 343 cells, 35 m each of length, for a
total of 12,005 m, and the modeled length in the cross-shore direction comprises 80 cells,
28.75 m width each, for a total of 2300 m

12000

11000

10000

9000

E 8000

S7000

5 6000

0
S5000

= 4000

3000

2000

1000

Pit Centerline

I I I

3

f

? I I I I I I r I I I T I

. I, I . I 1 , ,

I I

%0

0.5
Breaking Wave Height (m)

Figure 6.10 Breaking wave height after smoothing at Grand Isle
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds)

12000

11000

10000

9000

E 8000

S7000

5 6000

5000

=. 4000
CO
3000

2000

1000

nt1

Pit Centerline

SI

. .I I I I I I I

-10 -5 0 5 10
Breaking Wave Angle (degree)

Figure 6.11 Breaking wave angle after smoothing at Grand Isle
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds)

i I

12000

11000

10000

9000

E 8000

r 7000

S6000

0
S5000

. 4000

3000

2000

1000

0

MM

0
Shoreline Change (m)

Figure 6.12 Shoreline change for a normal incident wave after smoothing
(Pit centerline at 6000 m offshore)
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds at Grand Isle)

i n I I I I I I I

SI

I

12000

11000

10000

9000

8000

S7000

a 6000

5000 o

4000

3000

2000

1000

-15 -10 -5 0 5 10
Shoreline Change (m)

Figure 6.13 Shoreline change for incident wave angle equal to 6.5 degree after smoothing
(Pit centerline at 6000 offshore)
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds at Grand Isle)

8000

7000

0 a (Positive)
6000
6. a (Negative)

5000

4000

0 1000 2000 3000 4000 5000
Offshore Distance (m)

Figure 6.14 Wave rays for smoothed pit at Grand Isle and definition sketch
for wave angle direction at Grand Isle
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds)

6.4 Adding Second Term in "CERC" Equation and Comparing the Results

Chapter 4 presented a form of the CERC equation which included only one term

which represents sediment transport due to obliquely incident breaking waves. However,

a second term represents the transport contribution produced by longshore currents

resulting from a gradient in wave-setup if breaking wave heights vary in the longshore

direction (Ozasa and Brampton, 1980). The full CERC transport equation as follows,

shoreline changes including the second term are only slightly smaller than that with only

the first term included.

12000

11000

10000

9000

S8000

7000

6000

5000

4000

3000

2000

1000

-- Including First Term Only
- -- Including First and Second Terms

Shoreline Change (m)

Figure 6.15 Comparing the results of simplified CERC and full CERC equations normal
incident waves at Grand Isle
(Water depth, h, of 15 feet, incident waves with a wave height of 1.5 feet
and a period of 5.6 seconds)

CHAPTER 7
SOME GENERAL RESULTS FOR IDEALIZED CASES

7.1 Introduction

As much as 90 percent of the sand for beach nourishment projects is obtained from

offshore sources. In these areas, sediment sizes are often reasonably compatible with the

beach that is to be nourished. These offshore areas can be located small or large (tens of

kilometers) distances from the beach to be nourished. The excavated depths of borrow

pits are also different. Regardless of their geometries and locations, borrow pits can affect